Easiest thing I've seen is Cyclops (Joe W Rea's) idea. Buy a bore snake, take the brush out (it'll damage the internal O-Rings) and use a bore snake. Might have to cut the weight off depending on the breach. Put some cleaner on it and clean away. Couple pulls and done. best part is that there's nothing that can damage the crown.
https://www.youtube.com/watch?v=Xbc7kqnKg6Y
Here's another opinion:
https://www.youtube.com/watch?v=fFpIxuzr8UM
And another
https://www.youtube.com/watch?v=5xu6ZnX7q4M
I like the brushless bore snakes. You can buy Boresnakes on eBay for something like $2 each. I bought a bunch in all calibers a while back.
Using this system, there's no way you can hurt the crown.
If you have a PCP, you'll need to cut the weight off because it's too long for the breach. I usually run a loop of weed eater string from the muzzle, hoot over the end of the bore snake and pull it all through. 2 or 3 pulls and you are done.